I am going to preface this question with the fact that yes, I am well aware they are separate AC calculations that you choose between. I am simply posing a theoretical question that warrants deeper thought.
With that being said, while I was reviewing the Sorcerer class features in preparation for a session today, I had a thought: Lizardfolk's Natural Armor is equal to 13 + Dex. mod because of their naturally thick hide. Barbarian's Unarmored Defense is equal to 10 + Dex. + Con. mods because of their (courage or pure anger)1.
In my mind, allowing a Lizardfolk Barbarian to have their AC be equal to 13 + Dex. + Con. (+ shield) makes complete sense, as it's not like the Monk's Unarmored Defense where the Wis. mod is for them being more (studied in finesse and knowing where to be to dodge an attack)1.
What would be the impact if I ruled that the Lizardfolk's Natural Armor stacked with Barbarian's Unarmored Defense?
1Someone replace these parts in parentheses with the actual lore reason, I can't figure it out. Also delete this footnote once no longer relevant!